Abstract
We introduce and study a variant of Ramsey numbers for edge-ordered graphs, that is, graphs with linearly ordered sets of edges. The edge-ordered Ramsey numberR¯e(G) of an edge-ordered graph G is the minimum positive integer N such that there exists an edge-ordered complete graph KN on N vertices such that every 2-coloring of the edges of KN contains a monochromatic copy of G as an edge-ordered subgraph of KN.We prove that the edge-ordered Ramsey number R¯e(G) is finite for every edge-ordered graph G and we obtain better estimates for special classes of edge-ordered graphs. In particular, we prove R¯e(G)≤2O(n3logn) for every bipartite edge-ordered graph G on n vertices. We also introduce a natural class of edge-orderings, called lexicographic edge-orderings, for which we can prove much better upper bounds on the corresponding edge-ordered Ramsey numbers.
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
